Math Problem Statement

Реши и объясни

Какое из чисел отмечено на координатной прямой точкой B?

Solution

The problem asks to determine which number corresponds to point B on the coordinate line.

Point B is located at the position 2 on the number line. The four answer choices are square roots of numbers:

A) 2\sqrt{2}
B) 3\sqrt{3}
C) 5\sqrt{5}
D) 6\sqrt{6}

We need to check which of these values is closest to 2. Here are the approximate values of the square roots:

  • 21.41\sqrt{2} \approx 1.41
  • 31.73\sqrt{3} \approx 1.73
  • 52.24\sqrt{5} \approx 2.24
  • 62.45\sqrt{6} \approx 2.45

Among these, the closest value to 2 is 4\sqrt{4}, but that is not in the answer choices. However, the closest approximation from the provided options is 5\sqrt{5}, which is approximately 2.24.

Thus, the correct answer is C) 5\sqrt{5}.

Do you need more details or have any questions?

Here are five related questions to think about:

  1. How can we estimate square roots without a calculator?
  2. What is the value of 4\sqrt{4} and why is it relevant here?
  3. How would the answer change if point B were located at 3 on the number line?
  4. Can you think of other ways to visually represent irrational numbers like 5\sqrt{5}?
  5. How do the square roots of non-perfect squares behave on a number line compared to perfect squares?

Tip: When estimating square roots, you can always look for perfect squares near the number you are approximating to get a rough idea.

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Math Problem Analysis

Mathematical Concepts

Number Line
Square Roots
Irrational Numbers
Approximation

Formulas

Square Root Approximation

Theorems

Properties of Real Numbers

Suitable Grade Level

Grades 6-8